Living needs are the needs people generate in their daily lives for survival and well-being. On life service platforms like Meituan, user purchases are driven by living needs, making accurate living need predictions crucial for personalized service recommendations. Traditional approaches treat this prediction as a closed-set classification problem, severely limiting their ability to capture the diversity and complexity of living needs. In this work, we redefine living need prediction as an open-set classification problem and propose PIGEON, a novel system leveraging large language models (LLMs) for unrestricted need prediction. PIGEON first employs a behavior-aware record retriever to help LLMs understand user preferences, then incorporates Maslow’s hierarchy of needs to align predictions with human living needs. For evaluation and application, we design a recall module based on a fine-tuned text embedding model that links flexible need descriptions to appropriate life services. Extensive experiments on real-world datasets demonstrate that PIGEON significantly outperforms closed-set approaches on need-based life service recall by an average of 19.37%. Human evaluation validates the reasonableness and specificity of our predictions. Additionally, we employ instruction tuning to enable smaller LLMs to achieve competitive performance, supporting practical deployment.